Can Radiators and Faux Facade Summon Father Winter?

All the radiators and the Faux Fireplace Facade item are listed in the Fireplaces category. If you have one of these in your home, will Father Winter appear on Winterfest, or do you absolutely need one of the actual fireplaces that look and act like fireplaces? I assume Space Heaters wouldn't. They aren't even in that category, though they're functionally the same as a radiator. If those don't summon him, why did they put them in that category? That would be so misleading.